### New from this chapter

$$P \cdot V_{\mathrm{gas}} = n \cdot R \cdot T$$      chemical amount of a pure gas (ideal gas law)

$$P_{\mathrm{component}} \cdot V_{\mathrm{gas}} = n_{\mathrm{component}} \cdot R \cdot T$$      chemical amount of a gas component

$$P_{\mathrm{total}} = \sum (P_{\mathrm{partial}})$$      Additivity of partial pressure

$$X_{\mathrm{A}} = \dfrac{n_{\mathrm{A}}}{n_{\mathrm{total}}}$$      definition of mole fraction

$$E_{\mathrm{kin\ avg}} = \dfrac{3}{2} \cdot R \cdot T$$      average molar kinetic energy of particle at given temperature

$$P_{\mathrm{A}} = X_{\mathrm{a}} \cdot P_{\mathrm{total}}$$      partial pressure from mole fraction

$$P = \dfrac{F}{A}$$      Definition of pressure

$$P_{\mathrm{hydrostatic}} = h \cdot ρ_{\mathrm{fluid}} \cdot g_{\mathrm{0}}$$      Hydrostatic pressure

$$\mathrm{rate}_{\mathrm{diffusion}} = \dfrac{n_{\mathrm{gas\ area}}}{Δt}$$      definition of rate of diffusion

$$\dfrac{\mathrm{rate}_{\mathrm{effusion\ A}}}{\mathrm{rate}_{\mathrm{effusion\ B}}} = \sqrt{\dfrac{m_{\mathrm{B}}}{m_{\mathrm{A}}}} = \sqrt{\dfrac{M_{\mathrm{B}}}{M_{\mathrm{A}}}}$$      molar mass dependence of rate of effusion

$$u_{\mathrm{rms}} = \sqrt{\dfrac{{u_{\mathrm{1}}}^{2} + {u_{\mathrm{2}}}^{2} + {u_{\mathrm{3}}}^{2} + {u_{\mathrm{4}}}^{2} \cdot ...}{n}}$$      definition of rms particle speed

$$u_{\mathrm{rms}} = \sqrt{\dfrac{2 \cdot E_{\mathrm{kin\ avg}} \cdot N_{\mathrm{A}}}{m_{\mathrm{particle}}}} = \sqrt{\dfrac{3 \cdot R \cdot T}{M_{\mathrm{particle}}}}$$      velocity of gas particle

$$Z = \dfrac{V_{\mathrm{molar\ measured}}}{V_{\mathrm{molar\ ideal}}} = \dfrac{P \cdot V_{\mathrm{molar\ measured}}}{R \cdot T}$$      non-ideality of gas

$$(P + \dfrac{{n}^{2} \cdot a}{{V_{\mathrm{gas}}}^{2}}) \cdot (V_{\mathrm{gas}} - n \cdot b) = n \cdot R \cdot T$$      non-ideal gas law

### From previous chapters

#### ...important for many chemistry topics (you should know these by heart)

chemical amount from mass of a pure substance
chemical amount of a solute
chemical amounts in a chemical reaction (stoichiometry)
finding the limiting reactant

#### ...might need one of those

$$ρ_{\mathrm{sample}} = \dfrac{m_{\mathrm{sample}}}{V_{\mathrm{sample}}}$$      Definition of density

$$N_{\mathrm{charge}} = N_{\mathrm{\ce{p+}}} - N_{\mathrm{\ce{e-}}}$$      protons and electrons have opposite charges

$$c_{\mathrm{1}} \cdot V_{\mathrm{1}} = c_{\mathrm{2}} \cdot V_{\mathrm{2}}$$      Dilution law

$$n_{\mathrm{1}} = ν \cdot n_{\mathrm{2}}$$      stoichiometric ratio (shortcut)

$$n_{\mathrm{1}} = ν_{\mathrm{1}} \cdot n_{\mathrm{\ce{->}}}$$      using chemical amount of reaction

$$\mathrm{Charge}_{\mathrm{species}} = \sum (N_{\mathrm{atom}} \cdot \mathrm{Ox}_{\mathrm{atom}})$$      Sum of oxidation number

$$n_{\mathrm{theoretical\ yield}} = n_{\mathrm{\ce{->}}} \cdot ν_{\mathrm{\ce{product}}}$$      calculating theoretical yield (based on chemical amount)

$$m_{\mathrm{theoretical\ yield}} = n_{\mathrm{\ce{->}}} \cdot ν_{\mathrm{\ce{product}}} \cdot M_{\mathrm{\ce{product}}}$$      calculating theoretical yield (by mass)

$$\mathrm{yield}_{\mathrm{rel}} = \dfrac{n_{\mathrm{actual}}}{n_{\mathrm{theoretical}}} \cdot 100\ \mathrm{％}$$      Calculating percent yield from amounts

$$\mathrm{yield}_{\mathrm{rel}} = \dfrac{m_{\mathrm{actual}}}{m_{\mathrm{theoretical}}} \cdot 100\ \mathrm{％}$$      Calculating percent yield from masses

#### ...less likely

$$N_{\mathrm{A}} = \dfrac{N_{\mathrm{particle}}}{n_{\mathrm{particle}}}$$      definition Avogadro's constant

$$\mathrm{fraction}_{\mathrm{bymass}} = \dfrac{m_{\mathrm{solute}}}{m_{\mathrm{solution}}} \cdot 100\ \mathrm{％}$$      definition concentration as mass fraction in percent

$$\mathrm{fraction}_{\mathrm{byvolume}} = \dfrac{V_{\mathrm{solute}}}{V_{\mathrm{solution}}}$$      definition concentration as volume fraction in percent

$$\mathrm{ppm} = \dfrac{1}{1000000}$$      definition ppm

$$\mathrm{ppb} = 1\times 10^{-9}$$      definition ppb

$$N_{\mathrm{atoms}} = \mathrm{coeff} \cdot \mathrm{subscript}$$      Counting atoms in formula or chemical equation

$$ΔU = q + w$$      First law of thermodynamics

$$ΔH_{\mathrm{reaction}} = \sum (n_{\mathrm{prod}} \cdot ΔH_{\mathrm{f,prod}}) - \sum (n_{\mathrm{react}} \cdot ΔH_{\mathrm{f,react}})$$      Enthalpy from heats of formation

$$E_{\mathrm{photon}} = h_{\mathrm{Planck}} \cdot ν$$      Photon: Energy vs frequency

$$\mathrm{charge}_{\mathrm{formal}} = ⋕e_{\mathrm{outer\ freeatom}} - ⋕e_{\mathrm{lonepairs}} - \dfrac{1}{2} \cdot ⋕e_{\mathrm{bonding}}$$      Definition of formal charge

$$D_{\mathrm{\ce{X-Y}}} = ΔH_{\mathrm{bonddissociation}}$$      Definition of bond energy

$$\mathrm{order}_{\mathrm{bond}} = \dfrac{⋕e_{\mathrm{bonding}} - ⋕e_{\mathrm{antibonding}}}{2}$$      definition bond order